Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$

$K$ is the global number field defined by \(x^{2} \) \(\mathstrut +\mathstrut 114 \)

$\times$ \(\chi_{ 456 } ( 1, ·)\) \(\chi_{ 456 } ( 227, ·)\)
\(\chi_{ 456 }(1, ·)\) \(\chi_{ 456 } ( 1, ·)\) \(\chi_{ 456 } ( 227, ·)\)
\(\chi_{ 456 }(227, ·)\) \(\chi_{ 456 } ( 227, ·)\) \(\chi_{ 456 } ( 1, ·)\)